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A055636 Partial sums of A144494. 2
0, 0, 0, 2, 2, 4, 4, 7, 9, 11, 11, 14, 14, 16, 18, 22, 22, 25, 25, 28, 30, 32, 32, 36, 38, 40, 43, 46, 46, 49, 49, 54, 56, 58, 60, 64, 64, 66, 68, 72, 72, 75, 75, 78, 81, 83, 83, 88, 90, 93, 95, 98, 98, 102, 104, 108, 110, 112, 112, 116, 116, 118, 121, 127, 129, 132, 132 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Excess of prime-power exponents in n!.
LINKS
FORMULA
a(n) = A046660(n!) = A046660(A000142(n)) = A022559(n) - A001221(n!) = A001222(n!) - A000720(n).
EXAMPLE
n=46: prime powers in factorization of 46! are {42,21,10,6,4,3,2,2,2,1,1,1,1,1}. Sum of the exponents is 97. It has 14 distinct prime divisors, so a(46)=97-14=83.
MATHEMATICA
Table[PrimeOmega[n!] - PrimeNu[n!], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)
PROG
(PARI) for(n=1, 100, print1(bigomega(n!) - omega(n!), ", ")) \\ G. C. Greubel, May 13 2017 *)
CROSSREFS
Sequence in context: A056503 A256217 A361439 * A206559 A143419 A183566
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 07 2000
EXTENSIONS
Simpler definition from Alan Worley (aw(AT)xiboo.co.uk), Dec 10 2008
STATUS
approved

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Last modified March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)